Direction discrimination was used to measure the minimum and maximum displacement for the detection of motion (Dmin and Dmax) for abruptly displaced sinewave gratings. This was measured for a range of contrast levels from 2 to 32 times the detection threshold for a range of spatially narrow band stimuli. Performance for Dmin (but not Dmax) was found to deteriorate with an increase in contrast, with the most sensitive values for Dmin obtained at contrast levels of 4-8 times detection threshold. This dependence on luminance contrast is thought to be due to the physiology of the visual system, rather than the physics of the stimulus.